概述
序列标注指给定输入序列,给序列中每个Token进行标注标签的过程。序列标注问题通常用于从文本中进行信息抽取,包括分词(Word Segmentation)、词性标注(Position Tagging)、命名实体识别(Named Entity Recognition, NER)等。
条件随机场(CRF)
对序列进行标注,实际上是对序列中每个Token进行标签预测,可以直接视作简单的多分类问题。但是序列标注不仅仅需要对单个Token进行分类预测,同时相邻Token直接有关联关系。
设为输入序列,
为输出的标注序列,输出序列y的概率为:
定义两个概率函数
1. 发射概率函数:表示
的概率
2. 转移概率函数:表示
的概率
于是可以得到Score的计算公式:
设标签集合为T,构造大小为的矩阵P,用于存储标签间的转移概率。
实现CRF层的前向训练部分,将CRF和损失函数做合并,选择分类问题常用的负对数似然函数,则有:
Score计算
def compute_score(emissions, tags, seq_ends, mask, trans, start_trans, end_trans):
# emissions: (seq_length, batch_size, num_tags)
# tags: (seq_length, batch_size)
# mask: (seq_length, batch_size)
seq_length, batch_size = tags.shape
mask = mask.astype(emissions.dtype)
# 将score设置为初始转移概率
# shape: (batch_size,)
score = start_trans[tags[0]]
# score += 第一次发射概率
# shape: (batch_size,)
score += emissions[0, mnp.arange(batch_size), tags[0]]
for i in range(1, seq_length):
# 标签由i-1转移至i的转移概率(当mask == 1时有效)
# shape: (batch_size,)
score += trans[tags[i - 1], tags[i]] * mask[i]
# 预测tags[i]的发射概率(当mask == 1时有效)
# shape: (batch_size,)
score += emissions[i, mnp.arange(batch_size), tags[i]] * mask[i]
# 结束转移
# shape: (batch_size,)
last_tags = tags[seq_ends, mnp.arange(batch_size)]
# score += 结束转移概率
# shape: (batch_size,)
score += end_trans[last_tags]
return score
Normalizer计算
Normalizer可以改写为以下形式:
Normalizer代码实现如下:
def compute_normalizer(emissions, mask, trans, start_trans, end_trans):
# emissions: (seq_length, batch_size, num_tags)
# mask: (seq_length, batch_size)
seq_length = emissions.shape[0]
# 将score设置为初始转移概率,并加上第一次发射概率
# shape: (batch_size, num_tags)
score = start_trans + emissions[0]
for i in range(1, seq_length):
# 扩展score的维度用于总score的计算
# shape: (batch_size, num_tags, 1)
broadcast_score = score.expand_dims(2)
# 扩展emission的维度用于总score的计算
# shape: (batch_size, 1, num_tags)
broadcast_emissions = emissions[i].expand_dims(1)
# 根据公式(7),计算score_i
# 此时broadcast_score是由第0个到当前Token所有可能路径
# 对应score的log_sum_exp
# shape: (batch_size, num_tags, num_tags)
next_score = broadcast_score + trans + broadcast_emissions
# 对score_i做log_sum_exp运算,用于下一个Token的score计算
# shape: (batch_size, num_tags)
next_score = ops.logsumexp(next_score, axis=1)
# 当mask == 1时,score才会变化
# shape: (batch_size, num_tags)
score = mnp.where(mask[i].expand_dims(1), next_score, score)
# 最后加结束转移概率
# shape: (batch_size, num_tags)
score += end_trans
# 对所有可能的路径得分求log_sum_exp
# shape: (batch_size,)
return ops.logsumexp(score, axis=1)
Viterbi算法
在完成前向训练部分后,需要实现解码部分。Viterbi算法与计算Normalizer类似,使用动态规划求解所有可能的预测序列得分。不同的是在解码时同时需要将第i个Token对应的score取值最大的标签保存,供后续使用Viterbi算法求解最优预测序列使用。
取得最大概率得分ScoreScore,以及每个Token对应的标签历史HistoryHistory后,根据Viterbi算法可以得到公式:
代码实现:
def viterbi_decode(emissions, mask, trans, start_trans, end_trans):
# emissions: (seq_length, batch_size, num_tags)
# mask: (seq_length, batch_size)
seq_length = mask.shape[0]
score = start_trans + emissions[0]
history = ()
for i in range(1, seq_length):
broadcast_score = score.expand_dims(2)
broadcast_emission = emissions[i].expand_dims(1)
next_score = broadcast_score + trans + broadcast_emission
# 求当前Token对应score取值最大的标签,并保存
indices = next_score.argmax(axis=1)
history += (indices,)
next_score = next_score.max(axis=1)
score = mnp.where(mask[i].expand_dims(1), next_score, score)
score += end_trans
return score, history
def post_decode(score, history, seq_length):
# 使用Score和History计算最佳预测序列
batch_size = seq_length.shape[0]
seq_ends = seq_length - 1
# shape: (batch_size,)
best_tags_list = []
# 依次对一个Batch中每个样例进行解码
for idx in range(batch_size):
# 查找使最后一个Token对应的预测概率最大的标签,
# 并将其添加至最佳预测序列存储的列表中
best_last_tag = score[idx].argmax(axis=0)
best_tags = [int(best_last_tag.asnumpy())]
# 重复查找每个Token对应的预测概率最大的标签,加入列表
for hist in reversed(history[:seq_ends[idx]]):
best_last_tag = hist[idx][best_tags[-1]]
best_tags.append(int(best_last_tag.asnumpy()))
# 将逆序求解的序列标签重置为正序
best_tags.reverse()
best_tags_list.append(best_tags)
return best_tags_list
CRF层
CRF的输入需要考虑输入序列的真实长度,因此除发射矩阵和标签外,加入 seq_length 参数传入序列Padding前的长度,并实现生成mask矩阵的 sequence_mask 方法。
代码实现:
import mindspore as ms
import mindspore.nn as nn
import mindspore.ops as ops
import mindspore.numpy as mnp
from mindspore.common.initializer import initializer, Uniform
def sequence_mask(seq_length, max_length, batch_first=False):
"""根据序列实际长度和最大长度生成mask矩阵"""
range_vector = mnp.arange(0, max_length, 1, seq_length.dtype)
result = range_vector < seq_length.view(seq_length.shape + (1,))
if batch_first:
return result.astype(ms.int64)
return result.astype(ms.int64).swapaxes(0, 1)
class CRF(nn.Cell):
def __init__(self, num_tags: int, batch_first: bool = False, reduction: str = 'sum') -> None:
if num_tags <= 0:
raise ValueError(f'invalid number of tags: {num_tags}')
super().__init__()
if reduction not in ('none', 'sum', 'mean', 'token_mean'):
raise ValueError(f'invalid reduction: {reduction}')
self.num_tags = num_tags
self.batch_first = batch_first
self.reduction = reduction
self.start_transitions = ms.Parameter(initializer(Uniform(0.1), (num_tags,)), name='start_transitions')
self.end_transitions = ms.Parameter(initializer(Uniform(0.1), (num_tags,)), name='end_transitions')
self.transitions = ms.Parameter(initializer(Uniform(0.1), (num_tags, num_tags)), name='transitions')
def construct(self, emissions, tags=None, seq_length=None):
if tags is None:
return self._decode(emissions, seq_length)
return self._forward(emissions, tags, seq_length)
def _forward(self, emissions, tags=None, seq_length=None):
if self.batch_first:
batch_size, max_length = tags.shape
emissions = emissions.swapaxes(0, 1)
tags = tags.swapaxes(0, 1)
else:
max_length, batch_size = tags.shape
if seq_length is None:
seq_length = mnp.full((batch_size,), max_length, ms.int64)
mask = sequence_mask(seq_length, max_length)
# shape: (batch_size,)
numerator = compute_score(emissions, tags, seq_length-1, mask, self.transitions, self.start_transitions, self.end_transitions)
# shape: (batch_size,)
denominator = compute_normalizer(emissions, mask, self.transitions, self.start_transitions, self.end_transitions)
# shape: (batch_size,)
llh = denominator - numerator
if self.reduction == 'none':
return llh
if self.reduction == 'sum':
return llh.sum()
if self.reduction == 'mean':
return llh.mean()
return llh.sum() / mask.astype(emissions.dtype).sum()
def _decode(self, emissions, seq_length=None):
if self.batch_first:
batch_size, max_length = emissions.shape[:2]
emissions = emissions.swapaxes(0, 1)
else:
batch_size, max_length = emissions.shape[:2]
if seq_length is None:
seq_length = mnp.full((batch_size,), max_length, ms.int64)
mask = sequence_mask(seq_length, max_length)
return viterbi_decode(emissions, mask, self.transitions, self.start_transitions, self.end_transitions)
BiLSTM+CRF模型
其中LSTM提取序列特征,经过Dense层变换获得发射概率矩阵,最后送入CRF层。具体实现如下:
class BiLSTM_CRF(nn.Cell):
def __init__(self, vocab_size, embedding_dim, hidden_dim, num_tags, padding_idx=0):
super().__init__()
self.embedding = nn.Embedding(vocab_size, embedding_dim, padding_idx=padding_idx)
self.lstm = nn.LSTM(embedding_dim, hidden_dim // 2, bidirectional=True, batch_first=True)
self.hidden2tag = nn.Dense(hidden_dim, num_tags, 'he_uniform')
self.crf = CRF(num_tags, batch_first=True)
def construct(self, inputs, seq_length, tags=None):
embeds = self.embedding(inputs)
outputs, _ = self.lstm(embeds, seq_length=seq_length)
feats = self.hidden2tag(outputs)
crf_outs = self.crf(feats, tags, seq_length)
return crf_outs
完成模型设计后,我们生成两句例子和对应的标签,并构造词表和标签表。
embedding_dim = 16
hidden_dim = 32
training_data = [(
"清 华 大 学 坐 落 于 首 都 北 京".split(),
"B I I I O O O O O B I".split()
), (
"重 庆 是 一 个 魔 幻 城 市".split(),
"B I O O O O O O O".split()
)]
word_to_idx = {}
word_to_idx['<pad>'] = 0
for sentence, tags in training_data:
for word in sentence:
if word not in word_to_idx:
word_to_idx[word] = len(word_to_idx)
tag_to_idx = {"B": 0, "I": 1, "O": 2}
接下来实例化模型,选择优化器并将模型和优化器送入Wrapper。
model = BiLSTM_CRF(len(word_to_idx), embedding_dim, hidden_dim, len(tag_to_idx))
optimizer = nn.SGD(model.trainable_params(), learning_rate=0.01, weight_decay=1e-4)
grad_fn = ms.value_and_grad(model, None, optimizer.parameters)
def train_step(data, seq_length, label):
loss, grads = grad_fn(data, seq_length, label)
optimizer(grads)
return loss
将生成的数据打包成Batch,按照序列最大长度,对长度不足的序列进行填充,分别返回输入序列、输出标签和序列长度构成的Tensor。
def prepare_sequence(seqs, word_to_idx, tag_to_idx):
seq_outputs, label_outputs, seq_length = [], [], []
max_len = max([len(i[0]) for i in seqs])
for seq, tag in seqs:
seq_length.append(len(seq))
idxs = [word_to_idx[w] for w in seq]
labels = [tag_to_idx[t] for t in tag]
idxs.extend([word_to_idx['<pad>'] for i in range(max_len - len(seq))])
labels.extend([tag_to_idx['O'] for i in range(max_len - len(seq))])
seq_outputs.append(idxs)
label_outputs.append(labels)
return ms.Tensor(seq_outputs, ms.int64), \
ms.Tensor(label_outputs, ms.int64), \
ms.Tensor(seq_length, ms.int64)
对模型进行预编译后,训练500个step。
from tqdm import tqdm
steps = 500
with tqdm(total=steps) as t:
for i in range(steps):
loss = train_step(data, seq_length, label)
t.set_postfix(loss=loss)
t.update(1)
最后将预测的index序列转换为标签序列,打印输出结果,查看效果。
idx_to_tag = {idx: tag for tag, idx in tag_to_idx.items()}
def sequence_to_tag(sequences, idx_to_tag):
outputs = []
for seq in sequences:
outputs.append([idx_to_tag[i] for i in seq])
return outputs
sequence_to_tag(predict, idx_to_tag)
得到输出标签
[['B', 'I', 'I', 'I', 'O', 'O', 'O', 'O', 'O', 'B', 'I'],
['B', 'I', 'O', 'O', 'O', 'O', 'O', 'O', 'O']]
总结
LSTM用于提取序列特征,CRF用于序列标注,从而实现语义的切分。
标签:25,seq,tags,19,batch,length,score,打卡,size From: https://blog.csdn.net/m0_62894627/article/details/140241748